{
  "id": "0910.0408",
  "version": "v1",
  "published": "2009-10-02T14:32:03.000Z",
  "updated": "2009-10-02T14:32:03.000Z",
  "title": "Composition operators on weighted Bergman spaces of a half plane",
  "authors": [
    "Sam Elliott",
    "Andrew Wynn"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We use induction and interpolation techniques to prove that a composition operator induced by a map $\\phi$ is bounded on the weighted Bergman space $\\A^2_\\alpha(\\mathbb{H})$ of the right half-plane if and only if $\\phi$ fixes $\\infty$ non-tangentially, and has a finite angular derivative $\\lambda$ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by $\\lambda^{(2+\\alpha)/2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-02T14:32:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33"
    ],
    "keywords": [
      "weighted bergman space",
      "composition operator",
      "half plane",
      "right half-plane",
      "interpolation techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0408E"
    }
  }
}